Mr. Smart is an investor with $ 15,000 to invest. He has narrowed his choice down to two possible investments:

Mutual fund

Common shares in Buyme Corporation

Figure 3.5 gives a decision tree for Mr. Smart’s situation. Mr. Smart is risk averse. The amount of utility he derives from a payoff is

Utility 5 2 ln( payoff)

where “ ln” denotes natural logarithm.

Because of a planned major purchase, Mr. Smart intends to sell his investment one year later. The payoffs represent the proceeds from the sale of the investment and receipt of any dividends, net of the initial investment. The probabilities on Figure 3.5 represent Mr. Smart’s prior probabilities about the state of the economy (good or bad) over the coming year.

Required

a. Calculate Mr. Smart’s expected utility for each action, and indicate which action he would choose if he acted on the basis of his prior information.

b. Now, suppose Mr. Smart decides that he would like to obtain more information about the state of the economy rather than simply accepting that it is just as likely to be good as bad. He decides to take a sample of current annual reports of major corporations.